General comments:

This paper investigates the circulation, temperature, and atmospheric energy balance responses to surface heating imposed at various latitudes in a moist, gray radiation, clear-sky aquaplanet model. The authors show the circulation responses to surface heating are latitude dependent. The circulation response to low latitude surface heating is characterized by time-mean vertical and horizontal temperature advection whereas the circulation response to high latitude heating is characterized by transient eddy heat flux divergence. They show the composition of the atmospheric energy balance response to surface heating is also latitude dependent, where atmospheric radiative cooling is increasingly important for balancing surface heating with increasing latitude due to the decreasing efficiency of circulation heat export and the temperature-dependence of the Planck feedback.

The analysis and findings presented are interesting and a useful addition to the literature on the circulation response to idealized forcings. Idealized model experiments are valuable for their interpretability but it is important to make clear if the understanding imparted therefrom are applicable to the real world or not. Specifically, I would like to see the authors check the robustness of their results in a control climate that more accurately represents that of the modern climate. I also have other minor comments below that I would like to see addressed prior to publication.

Specific comments:

Line 4: I suggest specifying “time-mean” or “stationary” circulation responses here to make more clear the contrast with the subsequent discussion on transient eddy heat flux divergence.

Fig. 1A: This approximately factor of 2 discrepancy in the transient eddy kinetic energy climatology between the idealized experiment and reanalysis is quite large. Since the results include the transient eddy heat flux response to surface heating perturbations, I think it is important to check if the results are robust in a model setup that more accurately captures the observed transient eddy kinetic energy climatology of the modern climate. Otherwise, the presented results may only be relevant to that of an equable climate with no sea ice instead of Earth’s modern climate. I suspect this discrepancy is likely due to the significantly weaker baroclinicity of a no sea-ice aquaplanet set up. If so, the discrepancy could be reduced by modifying the control climate Q-flux profile such that the resulting baroclinicity resembles that of modern Earth. For example, Miyawaki et al. (2023, Environ. Res.: Climate) introduced a simple way to include the thermodynamic effect of sea ice in the form of a climatological Q flux. Since the resulting meridional temperature profile, even in an aquaplanet with no sea ice model, has been shown to capture that of a climate that has sea ice, I suspect imposing such a Q flux profile will help reduce the discrepancy in transient eddy kinetic energy between the idealized experiment and the reanalysis as well.

Fig. S1 right column: It’s surprising to see the lack of a near-surface inversion over the high latitudes in the reanalysis. I was expecting this to be one of the discrepancies between the temperature profiles of an idealized model with no sea ice and reanalysis. How is subsurface data treated for reanalysis data? The fact that 1000 hPa data are shown over Antarctica makes me wonder if subsurface data are not masked. 

Fig. 1: Why is the outermost contour of each Q-flux profile not smooth? This seems unexpected from equation 1.

Fig. 9 and Section 3.4: I think it’s important that these results are accompanied by an additional methods subsection on the column-integrated atmospheric energy budget. The terms in Fig. 9 are not defined in the current manuscript. This new method subsection should make clear that the circulation (residual) term differs from the temperature advection terms in equation 2 because of the inclusion of other advected energy terms such as latent and geopotential energy in Fig. 9.

Fig. 9 and Section 3.4: Related to above, it would be helpful to have a discussion somewhere (perhaps in the aforementioned new method subsection) on why this section considers the moist static energy budget (where surface latent heat flux is a diabatic term) as opposed to the dry static energy budget (where column-integrated condensation, or precipitation is an adiabatic term). Considering the results up to this point are based on the dry static energy budget, why not keep things simple by sticking to the dry static energy budget for Fig. 9 and Section 3.4?

Line 217-220: This sentence is confusing to me. Isn’t the amplified high-latitude temperature response plausible due to an increased reliance on radiative cooling in the high latitudes in addition to the temperature dependence of the Planck feedback? They seem like two separate contributions/mechanisms to me but this sentence reads as if they are somehow related. If so, can this link be further elaborated?

Line 244-248: I think it’s important to specify here that you are referring to the surface temperature response. The results show the circulation has an important impact on the vertical structure of the temperature response in both the low and high latitudes.

Line 249-255: Given the highly idealized model setup of this study, I think it would be useful to specify how future studies could further investigate the robustness of the results across a hierarchy of complexity, such as the role of radiation spectroscopy (i.e., non-gray radiation) and clouds, in particular.

Technical comments:

Line 213, 215, and Fig. 9 caption: I believe the term “lateral” energy transport is used here to mean “horizontal” energy transport, which is the term that has been used throughout the manuscript up to this point. For consistency I suggest rephrasing lateral to horizontal.

Summary

This study uses an idealized moist GCM to examine the qualitative dependence of the atmospheric response to a localized large-scale surface heat source on the latitude of the heat source. The experimental setup is an idealized aqua-planet setup, without land, ice and clouds and with a gray-radiation parameterization. The equilibrated response is analyzed in terms of temperature, circulation and energy balance. The main findings, which are generally consistent with previous studies, show that the response in the tropics is mainly through convective processes, which transfer the heat upward and lead to energy flux out of the air column, whereas at high latitudes the response shows a strong heating of the surface and lower troposphere, which leads to increased outgoing longwave radiation. The authors suggest a link between these results and the phenomenon of polar amplification.

The manuscript is well-written, and the rational of the study is clear. I find the method adequate for addressing the research question. However, I find the discussion and concluding remarks a bit too vague and too short. I think this manuscript is fit for publication in WCD, in terms of the scientific scope. I suggest a few specific (rather minor) revisions prior to publication, as elaborated below.

Major comments

• Description of the model setup (subsection 2.1): Some details of the model setup and some discussion of those details are missing. (a) Does the model include a representation of clouds and their radiative effect? I suppose it doesn’t, but there is no discussion about the choice of using a model without clouds to study the energetic response to surface heating. Would you except to find significantly different results if clouds were included? It could affect the level from which longwave radiation is emitted to space, and thus affect the relation between surface temperature and OLR (lines 218-219). (b) It is mentioned that the model doesn’t include sea ice, but again – it is not mentioned whether the implications of the results for Arctic warming are affected by the absence of sea ice in the model. (c) What is the motivation for using a gray radiation model rather than a full radiation model, that gives a more realistic circulation (see Jucker and Gerber, 2017 and Tan et al. 2019)? (d) Why do you choose to use the TRACMIP protocol with diurnal and seasonal cycles? Eventually, only the climatological annual mean response is considered, so why do you choose to include the full cycles? (e) I suppose there is no land in these experiments, but it is confusing that the TRACMIP initials include the word “continent”. Is there land in the model or not?
• Equation 2: The time tendency term is omitted. It would be good to at least mention that this is an approximate equation, assuming a steady state. It is mentioned a few lines below that Q is calculated as a residual, and that it’s vertical integral is very close to the vertical integral of the diabatic heating, calculated as the sum of all the source terms. It is argued that “This confirms that the residual method provides a good estimate of the diabatic heating”, but it is not mentioned that this depends on the assumption that the system is in steady state, and that the variables are averaged over a long enough period so that the tendency term is negligible. Later, in figure 6, the terms in this equation are shown as a function of longitude and height. Is the tendency term negligible also locally or only when considering the vertical integral?
• The temperature response is shown at the surface as a function of longitude and latitude (figure 2) and as a longitude-height cross-section (figure 3), but the latitude-height profile is not shown. It would give a more complete picture to see the latitudinal distribution of the temperature response, not just at the surface, but also throughout the troposphere. The energy budget (figure 9) implies that in the tropical heating case, the energy is transported away from the source region. Does this energy transport heat the atmosphere at higher latitudes? A latitude-height cross-section of the temperature response would show that.
• Subsection 3.4 shows the vertically-integrated atmospheric energy budget (figure 9). It would help the reader if the relevant equation would be written explicitly. The residual is said to be equal to advection of energy by the time-mean circulation plus energy transport by transient eddies (line 214). If the full energy budget equation would be written down, it would help to see what exactly these terms are. It is said that these terms are discussed in the previous subsection, but there it was part of the potential temperature equation, which is not the same as the vertically-integrated atmospheric energy budget.
• Discussion and concluding remarks (section 6): This section contains statements that are not clear, and that their connection to the results is not clear (lines 240-242, 246-248). How are these results relevant to the connection between Arctic sea ice loss and Arctic amplification, if there is no sea ice in the model? Why does the reduced baroclinicity in the case of the high-latitude heating perturbation limit how much the reduced eddy activity can cool the perturbation region? Why are vertical and horizontal circulation responses expected to be less dependent on the temperature response at lower latitudes? Additionally, I would expect to find here some discussion about the limitations of the relevance of these results to the actual atmosphere, due to the absence of clouds and sea ice in the model. Further, it is not quite clear what part of the results is new, and what part is consistent (or non-consistent) with results of previous studies.

Minor comments

• Figure S4: I think this figure would be more appropriate to include in the main paper, rather than the supplementary material. It would also require adding some text to explain what it means. This is just a suggestion. But if not, perhaps it would be better to remove it, because showing the vorticity response without an explanation is not very informative.
• Lines 140-141: “Overall, mean meridional and vertical advections do not appear to play important roles in balancing high-latitude, near-surface heating perturbations”. At this point, it is still not shown, it is shown in the following sections.
• In all the places where “vertical temperature advection” is mentioned (e.g., Figure 6 – panel title and caption and lines 148, 237), it should be called “vertical potential temperature advection”. There is a great difference between vertical temperature advection and vertical potential temperature advection, as the latter includes the effect of heating/cooling by contraction/expansion.
• Line 155: the horizontal temperature advection has a similar role in the 15N and 30N simulations (Figure 6A,B), why do you say that it starts to play a role in the 30N simulation?
• The use of the word “help” (lines 163, 174) indicates that moving excess heat or offsetting the perturbation is a “good” thing. I suggest to replace with “moves excess heat” and “offsets the perturbation” or “acts to offset the perturbation”.
• Lines 220-221: It would help the reader to explain what “such a relationship” means, i.e., that because of the nonlinearity of the Stephan-Boltzmann relation between longwave radiation and temperature, for a given change in the longwave radiation, the temperature change required to create this change is greater at lower temperatures.
• Lines 229-230: It is not clear what you mean here by “lapse rate feedback” in the context of stronger near-surface warming at high latitudes and how it is related to the lack of vertical advection. This requires some explanation.

Language / typos

• Line 106: “from the upper to lower troposphere” – add “the” before “lower”.
• Line 215: “energy transport by circulation” – add “the” before “circulation”.

References

Jucker, M. and E. Gerber, 2017: Untangling the annual cycle of the tropical tropopause layer with an idealized moist model. Journal of Climate, 30 (18), 7339-7358.

Tan, Z., O. Lachmy and T. A. Shaw, 2019: The sensitivity of the jet stream response to climate change to radiative assumptions. J. Adv. Model. Earth Syst., 11 (4), 934-956.

Title: Circulation responses to surface heating and implications for polar amplification 

Authors: Peter Yu-Feng Siew, Camille Li, Stefan Pieter Sobolowski, Etienne Dunn-Sigouin, and Mingfang Ting

Summary: This study employs a moist, gray radiation model to investigate the atmospheric response to tropospheric heating perturbations at different latitudes. The findings largely align with those presented by Hoskins and Karoly (1981), but additionally shed light on the significance of transient eddy heat flux divergence in high-latitude scenarios, particularly. The subject matter is both intriguing and significant, enhancing our comprehension of the dynamic impacts of high-latitude thermal forcings. Overall, the manuscript is well-written. I provide a few major and minor comments below for the authors' consideration.

Major comments:

1. In the initial sections of the manuscript, the authors scrutinized the complete thermodynamic equation and asserted that transient eddy heat flux divergence is the primary mechanism influencing polar circulation response (as depicted in Figure 6). However, in the subsequent portions, where the authors compared dynamical and radiative adjustment processes, the importance of the circulation component decreases as the forcing location shifts to higher latitudes (as illustrated in Figure 9). How could we reconcile these seemingly conflicting results? I guess there may be not necessary of conflict, but just interpretation from different perspective. Could the authors offer additional explanation or engage in further discussion?
2. In the model utilized for this study, the absence of water vapor feedback is notable due to the imposition of a single optical thickness across the entire long wave frequency band. However, recent studies have delved into the role of water vapor feedback in both attenuating and intensifying polar amplification (e.g., Beer and Eisenman 2022; Chung and Feldl 2023; Feldl and Merlis 2023). I am intrigued by how the incorporation of water vapor feedback might alter the magnitude and spatial distribution of polar amplification and subsequently influence atmospheric circulation responses. Moreover, considering the direct impact of water vapor on atmospheric circulation, could the authors provide further insights into these aspects?

Minor comments:

Lines 8-10: how could tell the cause and effect? Is sea ice loss a cause or effect?

Line 70: why the eddies in the upper troposphere appear to be weaker in the model? Is this related to vertical resolution in the model?

Line 84: how do you derive 450TW? 

Line 149: why the sign of the sum of the heart transport terms (blue color shading) is opposite from that of the diabetic heating (red color shading)? Is there a missing factor of -1?

Line 149 and Figure 6: could the authors plot out the sum of the heart transport terms?

Line 155: in the 30N case, the horizontal temperature advection has already presented some signals? And the role of eddies seems somewhat similar in 30N and 15N cases near surface.

Line 225: what does the global uniform heating refer to as? Well-mixed GHG forcing?

References:

Beer, E. and Eisenman, I., 2022. Revisiting the role of the water vapor and lapse rate feedbacks in the Arctic amplification of climate change. Journal of Climate, 35(10), pp.2975-2988.

Chung, P.C. and Feldl, N., 2023. Sea ice loss, water vapor increases, and their interactions with atmospheric energy transport in driving seasonal polar amplification. Journal of Climate, pp.1-28.

Feldl, N. and Merlis, T.M., 2023. A Semi‐Analytical Model for Water Vapor, Temperature, and Surface‐Albedo Feedbacks in Comprehensive Climate Models. Geophysical Research Letters, 50(21), p.e2023GL105796.